Added Recursive Binary Search Algorithm

binary_search_recursive.py

@@ -0,0 +1,62 @@
+"""Recursive approach of binary search.
+   Ref : https://en.wikipedia.org/wiki/Binary_search_algorithm
+
+   Time Complexity : O(log n)
+   Space Complexity : O(1)
+"""
+
+
+def find_index(nums: list, k: int, left: int, right: int) -> int:
+    """_summary_
+    Args:
+        nums (list): list of numbers
+        k (int): number to be find from the list
+        left (int): lower bound
+        right (int): upper bound
+    Returns:
+        int: index of k in list or -1 if k is not found in list
+    Examples
+    --------
+    >>> find_index([1,4,5,6,7],6,0,5)
+    3
+    >>> find_index([1,4,5,6,7],2,0,5)
+    -1
+    """
+    # Base case
+    if left >= right:
+        return -1
+
+    else:
+        mid = (left + right) // 2
+
+        if nums[mid] == k:
+            return mid
+        elif nums[mid] > k:
+            return find_index(nums, k, left, mid)
+        else:
+            return find_index(nums, k, mid + 1, right)
+
+
+def binary_search(nums: list, k: int, n: int) -> int:
+    """This function uses divide & conquer paradigm to find the number in a sorted list
+     and return its index.
+    Args:
+        nums (list): list of numbers
+        k (int): number to be find from the list
+        n (int): size of list
+    Returns:
+        int: index of k or -1 if k is not present in list
+    Examples
+    --------
+    >>> binary_search([1,4,5,6,7],6,5)
+    3
+    >>> binary_search([1,4,5,6,7],3,5)
+    -1
+    """
+    left = 0
+    right = n
+
+    return find_index(nums, k, left, right)
+
+
+print(binary_search([1, 4, 5, 6, 7], 6, 5))